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Find the derivative of F(x) = (8x^3 - 1)/(2x - 1), is this right?

  1. Oct 14, 2007 #1
    1. The problem statement, all variables and given/known data
    22. Divide the expression before differentiating.

    F(x) = (8x^3 - 1)/ (2x - 1)



    2. Relevant equations
    F'(x) = An^(x-1)


    3. The attempt at a solution

    F(x) = [(8x^3) / (2x - 1)] - [(1)/(2x - 1)]
    = [(4x^2)/(1)] - [(1) / (2x - 1)]
    = (4x^2) - (2x-1)^-1

    F'(x) = (8x + 1)
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 15, 2007 #2

    malawi_glenn

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    Science Advisor
    Homework Helper

    2. Relevant equations
    F'(x) = An^(x-1)

    ?

    And this is wrong:
    F(x) = [(8x^3) / (2x - 1)] - [(1)/(2x - 1)]
    = [(4x^2)/(1)] - [(1) / (2x - 1)]

    And even if that was right; the derivative of (4x^2) - (2x-1)^-1
    is not (8x + 1)

    The general rule for differentiation these kinds of functions are: x^n = n x^(n-1) Then you have rules for inner- and outer derivatives. I suggest you do the division of F(x) again, if you dont remember how to divide polynomials, you should look it up again.
     
  4. Oct 15, 2007 #3
    try this instead: (regard this as long division, not a square root!)

    2x-1 [tex]\sqrt{8x^3+0x^2+0x-1}[/tex]

    And remember, whatever you get in the end, your derivative has a discontinuity at x=1/2!
     
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